Find the complex number z such that `z^2+|z|=0`

Find the complex number z satisfying R e(z^2 =0),|z|=sqrt(3.)

Find the locus of a complex number z such that arg ((z-2)/(z+2))= (pi)/(3)

Find the complex number z satisfying R e(z^2) =0,|z|=sqrt(3.)

If the complex number z is such that |z-1|le1 and |z-2|=1 find the maximum possible value |z|^(2)

If z_1,z_2,z_3 are three complex numbers such that |z_1|=|z_2|=1 , find the maximum value of |z_1-z_2|^2+|z_2-z_3|^2+|z_3+z_1|^2

The number of complex numbers z such that |z-1|=|z+1|=|z-i| is

Let z=1+ai be a complex number, a > 0 ,such that z^3 is a real number. Then the sum 1+z+z^2+...+ z^11 is equal to:

If z_1, z_2, z_3 are three complex numbers such that 5z_1-13 z_2+8z_3=0, then prove that [(z_1,(bar z )_1, 1),(z_2,(bar z )_2 ,1),(z_3,(bar z )_3 ,1)]=0

If z is a complex number such that |z-1|= |z+1| , show that Re(z)= 0

Find the complex number z if zbarz = 2 and z + barz=2